\documentclass[
	solutions,
	singlenumbering,
	nopagenumber
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}


\makeatletter
\newcommand{\thisone}{
	\if@solutions
	{\color{red} $\Leftarrow$ \texttt{this one}}
	\else\fi
}

\title{Warm-Up: The Gallery}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today}

\begin{document}

	\maketitle

	A museum curator is arranging seven photographs on a gallery wall in accordance with the photographer's requirements.
	They are titled as follows: Fence, Gardenias, Hibiscus, Irises, Katydid, Lotus, and Magnolia.

	The photograph's requirements are as follows:
	\begin{itemize}
		\item Gardenias must be immediately before Katydid.
		\item Hibiscus must be somewhere before Katydid but cannot be the first photograph.
		\item Irises and Lotus must be next to one another.
		\item Magnolia must be one of the first three photographs.
		\item Fence must be either first or seventh.
	\end{itemize}

	\problem{}
	Which of the below could be a valid ordering? \par
	\note[Note]{We denote each painting by the first letter of its title.}
	\begin{itemize}
		\item \texttt{FHGMKIL}
		\item \texttt{HMGKILF}
		\item \texttt{ILMHGKF} \thisone{}
		\item \texttt{LMIHGKF}
		\item \texttt{MFHGKLI}
	\end{itemize}
	\vfill

	\problem{}
	If Irises is immediately before Gardenias, which of the following could be true?
	\begin{itemize}
		\item Gardenias is fourth
		\item Hibiscus is fourth
		\item Irises is third
		\item Lotus is second
		\item Magnolia is third \thisone{}
	\end{itemize}
	\vfill

	\problem{}
	The ordering of the photographs is fully determined if...
	\begin{itemize}
		\item Gardenias is fourth
		\item Hibiscus is second
		\item Irises is second
		\item Lotus is first \thisone{}
		\item Magnolia is third
	\end{itemize}

	\vfill
	\pagebreak

	\problem{}
	If Magnolia is second, what CANNOT be true?
	\begin{itemize}
		\item Hibiscus is third
		\item Hibiscus is fourth \thisone{}
		\item Hibiscus is fifth
		\item Gardenias is fourth
		\item Gardenias is sixth
	\end{itemize}

	\vfill

	\problem{}
	Katydid cannot be in which position?
	\begin{itemize}
		\item Third \thisone{}
		\item Fourth
		\item Fifth
		\item Sixth
		\item Seventh
	\end{itemize}
	\vfill

	\problem{}
	If Gardenias is fourth, what must be true?
	\begin{itemize}
		\item Fence is first \thisone{}
		\item Hibiscus is third
		\item Irises is seventh
		\item Magnolia is first
		\item Magnolia is second
	\end{itemize}
	\vfill

	\problem{}
	Which one of the following,
	if substituted for the second condition,
	would have the same effect in determining the
	arrangement of the photographs?

	\begin{itemize}
		\item If Fence is seventh, Hibiscus is second
		\item Gardenias is somewhere after Hibiscus, and either Fence or Magnolia is first
		\item Hibiscus must be somewhere between the first and sixth photographs
		\item Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias \thisone{}
		\item Katydid is somewhere after Hibiscus, which must be after Fence.
	\end{itemize}
	\vfill
	\pagebreak
\end{document}